1.6 & 1.7: Relations and Functions

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y).

Front

What is a function?

Back

A function is a special type of relation where each input (x) is associated with exactly one output (y).

Front

How can you determine if a relation is a function using the vertical line test?

Back

If a vertical line intersects the graph of the relation at more than one point, then the relation is not a function.

Front

What is the definition of a mapping in mathematics?

Back

A mapping is a way to describe a function by showing how each input is paired with an output.

Front

Evaluate f(4) if f(x) = 4x + 5.

Back

f(4) = 4(4) + 5 = 21.

Front

Evaluate f(-5) if f(x) = -2x - 12.

Back

f(-5) = -2(-5) - 12 = -2.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point in a coordinate system.

Front

What does it mean for a relation to be one-to-one?

Back

A one-to-one relation is a function where each output (y) is paired with exactly one input (x), and no two inputs share the same output.

Front

What is a table of values in relation to functions?

Back

A table of values lists pairs of input (x) and output (y) values for a function.

Front

What is the difference between a function and a non-function?

Back

A function has one output for each input, while a non-function may have multiple outputs for a single input.